WASHINGTON—Congressional Democrats said they reached a deal with President Donald Trump to give legal status to undocumented immigrants who were brought to the U.S. as children, but Mr. Trump on Thursday morning said no deal had been reached.

In a series of tweets Mr. Trump said there had been no agreement but he repeated his desire to aid this group of young immigrants who are currently protected by a program that he moved to end last week.

On Wednesday, Senate Minority Leader Chuck Schumer (D., N.Y.) and House Minority Leader Nancy Pelosi (D., Calif.) said in a joint statement that, over dinner at the White House, they had agreed with Mr. Trump on the outlines of a deal to enshrine protections for…